Under what circumstances is a very small treatment effect still likely to be statistically significant?
A) If the sample size is small and the sample variance is small
B) If the sample size is small and the sample variance is large
C) If the sample size is large and the sample variance is small
D) If the sample size is large and the sample variance is large

Question

Quizplus · Accepted Answer

When the sample size is large and the sample variance is small, it increases the power of the statistical test to detect even very small treatment effects as statistically significant. A larger sample size reduces the sampling error (i.e., variability between the sample mean and the population mean), while a smaller variance reduces the error within the sample (i.e., variability between individual data points in the sample). These factors increase the precision and accuracy of the estimates, allowing for the detection of significant differences even if they are very small.

Under What Circumstances Is a Very Small Treatment Effect Still